Archimedes Fun
It can be so much fun to study a person in history by looking at what things he has done. Even people like mathematicians, which are not always thought of as fun. Take Archimedes, for example. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. A new crown had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. The submerged crown would displace an amount of water equal to its own volume. By dividing the weight of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" meaning in Greek "I have found it!"
With this story in mind, we set up a simple demonstration to show this concept. Don't worry no bathtub involved. We took a bowl and set it in a baking dish. We then filled the bowl to the brim with water.
We then took two objects of almost identical weight. 
We determined that the rubber ball symbolized the lump of gold, and placed it in the bowl of water. It displaced a certain amount of water. 
We then placed our candle, which represented the crown, and we saw that it displaced some more water, showing that although its weight was similar, its density was not.
We determined that the rubber ball symbolized the lump of gold, and placed it in the bowl of water. It displaced a certain amount of water. We then placed our candle, which represented the crown, and we saw that it displaced some more water, showing that although its weight was similar, its density was not.
Update: I have found out that both 4 quarters and 5 Hershey's Chocolate Kisses weigh 1 ounce, so these can be used. You can use a postal scale if you have one, to prove this as part of your experiment. Carry out the experiment the same as above and you should see that the candies have more mass and displace more water.
Archimedes also was the first to study balance or the center of gravity of shapes. I had out a few triangles with different angles and asked him to draw lines from the corners to the middle of the side opposite it. The lines intercepted in the middle. Then, giving the boys the triangles with the lines down, I asked the boys to balance the triangles on the tips of their fingers...
then we looked under the triangles to see where their fingers were.
Archimedes also was the first to study balance or the center of gravity of shapes. I had out a few triangles with different angles and asked him to draw lines from the corners to the middle of the side opposite it. The lines intercepted in the middle. Then, giving the boys the triangles with the lines down, I asked the boys to balance the triangles on the tips of their fingers...
then we looked under the triangles to see where their fingers were.
The results were the same with all the triangles...
much to their delight.
Resources:
- Living Math.
- A fun book to read is Archimedes and the Door of Science.
- Another fun and simple experiment involving buoyancy is from Almost Unschoolers.
